I did discover you can add games to your library via the website, then sync your library in the app to download them from the Library section. However, this doesn't work for all games. Some will not sync with the desktop app and only appear in your library on the website. You can also still install stuff from the Viveport VR app, which launches Viveport in a VR environment. You can also download from there, but again, this doesn't work for all games. Some simply don't appear in the Viveport VR app, even using a search for specific titles or checking the game's genre. They do show up if I search for them in the desktop app, but of course, the Play/Download buttons are broken and don't do anything or don't appear at all.
I was able to get ~10 games installed this way, but I have 4 that are in my library on viveport.com, but don't appear in my library on the desktop or VR app and don't appear in the store at all in the VR app.
I sent a ticket in describing the issue, but support just sent me a predef asking me what time the problem occurred (if they'd actually read the message, they'd know it's been doing it at least since Friday and still doesn't work today). I pointed them to this thread in my reply, but who knows if they'll actually look. Their Twitter and these forums are silent about it, no idea if anyone's even noticed it, much less started working on it.